Symmetric and Geometric Methods

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Symmetry has played a ubiquitous role in our civilization throughout all ages. Mankind has been fascinated by the inherent beauty of symmetry in nature and has explored and searched for understanding its implications in his culture. This preoccupation with symmetry has led to discovery of rich mathematical theories to explain and apply symmetry in a vast number of subjects ranging from anthropology and the arts to engineering and the sciences. This project proposes to use symmetry and geometric methods in the sciences, the arts and engineering as a theme to develop topic-oriented course-modules that can be adapted in revitalizing undergraduate education in mathematics and other subjects. It is proposed to expose and explore some of these theories in their context of discovery and applications, constantly drawing attention to the quantitative and qualitative geometric methods that accompany the intuitive reasoning. It is reasonable to expect that a number of students will be attracted to engineering, mathematics and the sciences through their experience with such material. The proposed lab portion of the course-modules intends to get the students involved hands-on in exploring modern and advanced topics that are inaccessible in the present linearly ordered college curriculum, especially those that requires prerequisites from several mathematics and science courses.